Detecting operational anomalies for continuous hydraulic fracturing monitoring

ABSTRACT

A method for detecting operating anomalies during hydraulic fracturing includes inducing tube waves in a well during pumping a hydraulic fracture treatment. At least one of pressure and time derivative of pressure in the well is measured. The measured at least one of pressure and time derivative of pressure is transformed into the cepstrum domain. An operational anomaly is detected by determining a change in cepstral quefrency corresponding to a two-way travel time of the tube waves and resonances in the well.

CROSS REFERENCE TO RELATED APPLICATIONS

Continuation of International Application No. PCT/US2020/043175 filed on Jul. 23, 2020. Priority is claimed from U.S. Provisional Application No. 62/877,476 filed on Jul. 23, 2019. Both the foregoing applications are incorporated herein by reference in their entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT

Not Applicable.

BACKGROUND

This disclosure relates to the field of hydraulic fracturing of subsurface reservoir formations. More specifically, the disclosure relates to measuring properties of resonances and tube waves propagating in a well during fracture treatment to diagnose possible difficulties in a fracturing operation.

Hydraulic fracturing is a completion method designed to improve the productivity of wells by enhancing the fluid connection of the well to a subsurface reservoir. Fractures are created by injection of high pressure fluids, with carefully controlled injection rates and fluid properties (e.g., viscosity, density, and compliance) and with various added solutes, e.g., acids or solids, and quartz or other controlled-size particulates (proppant). During pumping, typical measurements made at the surface include fluid flow rate, proppant and chemical concentrations, and pressure. Such measurements may be digitally sampled to provide “pumping data” at digital sample frequencies of at most a few samples per second. Along with the information regarding the amounts of fluid and proppant pumped, these measurements often constitute the sole and primary means of monitoring what is occurring in the well and the reservoir.

Surface equipment and wellbore components have maximum safe operating pressures. Thus predicting the risk of flow restrictions in the borehole is important to avoid exceeding these maximum pressures to prevent damage to equipment or environment.

Operational problems such as difficulties delivering fluid at the required pumping rate) can be revealed by sudden and unexpected increases pressure. However, using current methods and data it can be difficult to quickly identify the source of such problems and thereby to select the appropriate solutions. Without additional information, identifying excessive pumping pressure is not always successful or timely enough to avoid problems. Other failures can occur such as leaks, isolation failures, etc., that are not revealed by pressure response until they are detected may cause a shutdown or failure. Moreover, occurrence of such problems may have significant negative impact on ultimate hydrocarbon production and recovery because the well may suffer reduced fluid production from the created hydraulic fracture network. Therefore, the ability to monitor the well and reservoir system to detect and characterize adverse events prior to failure would be important and valuable both to avoid costly downtime and also to achieve desired productivity improvements.

An example of a problem that can occur during fracturing operations is a screenout. A screenout occurs due to the buildup of solids, typically pumped proppant, in a portion of the flow path that impedes fluid motion and causes a rapid increase in pressure during continued fluid injection. The solids can build up anywhere in the system: in the well, the near-well region of fractures in the reservoir formation, or within the fractures themselves either close to or far from the well. When screenout occurs, pumping is halted while remedial operations are carried out, such as a “flowback” of several wellbore volumes, to remove the proppant (solids) from the well to re-establish a pathway for subsequent fracture fluid injection to complete the fracturing process. If the onset of proppant blockage in the near-well region and of proppant build-up at the bottom of the well could be detected during pumping operations (i.e., in real time) it would allow operators to stop injecting proppant before significant build-up occurs, thus enabling flushing out the build-up, and possibly avoiding the time-consuming and expensive process of having to remove such accumulated proppant inside the well when pumps are forced to shut down due to excessive pressure.

Methods known in the art rely on simple pressure monitoring during hydraulic fracturing treatment. A limitation to using pressure data alone to diagnose potential issues as they develop is that it is difficult to differentiate among various explanations for a particular pressure anomaly. For example, an increase in pressure could be due to a restriction anywhere within the system downstream of the pumps, including within or near the well. Such an increase could also occur at a distance from the well due to a restriction within a fracture being extended away from the well into the reservoir. Thus, it is desirable to have a method for detecting changes in the well or in the near-field of the well that can also differentiate those effects from changes at a distance from the well that produce similar indicators in pumping data, for example, increases in pressure. Earlier problem identification may allow for a higher chance of a successful recovery or outright avoidance of the problem.

Vibrational energy is created by fluid pumping and by the motion of fluids and solids, and this energy propagates throughout the well and tubing and interacts with the surroundings. This vibrational energy is efficiently propagated within the well, often in the form of guided waves, or tube waves, which are sensitive to properties of the well and the near-well region including of any connected fractures, and is relatively unaffected by properties including of the fracture system at a larger distance from the well. This vibrational energy is known to excite resonances in the wellbore and wellbore-fracture-system.

The characteristics of the vibrational energy, e.g., its frequency components and amplitudes, arrival times of pulses, and pulse shapes, are affected by the properties of the system including of the connection between the well and the evolving fracture system. However, this vibrational energy is seldom recorded and rarely used. Such is the case firstly, because this energy occurs at frequencies higher than can be measured with conventional fracture pumping data acquisition systems with sampling rates of no more than a few samples per second and secondly, because detecting coherent energy or signals that allows characterization of the well system is difficult due to the continuous presence of pumping and other noise.

Additionally, use of (exploiting) this data to monitor and react to identified system changes requires a rapid, near-real-time, robust means of analyzing and delivering the information about system characteristics to system operators. Multiple indicators are required to avoid false alerts and to provide information about the severity and likely time to occurrence of possible future events. Systems with the ability to acquire and display this data would be valuable because such systems would enable monitoring changes during operations to identify upcoming problems, to mitigate those problems by changing operations to prevent their occurrence, and to treat them while monitoring the treatments. This allows for continued, uninterrupted operation and successful delivery of hydraulic fracturing productivity improvements.

SUMMARY

One aspect of the present disclosure is a method for detecting operating anomalies during hydraulic fracturing. A method according to this aspect includes inducing tube waves in a well during pumping a hydraulic fracture treatment. At least one of pressure and time derivative of pressure in the well is measured. The measured at least one of pressure and time derivative of pressure is transformed into the cepstrum domain. An operational anomaly is detected by determining a change in cepstral quefrency corresponding to a two-way travel time of the tube waves in the well.

In some embodiments, the change in cepstral quefrency comprises a maximum value of quefrency.

In some embodiments, the change in cepstral quefrency comprises a minimum value of quefrency.

In some embodiments, the change in cepstral quefrency comprises a sum of a maximum and a minimum value of quefrency.

In some embodiments, the change of cepstral quefrency comprises a change in relative quefrency corresponding to a two-way travel time of a maximum and a minimum value of a quefrency. The lag time between the maximum and minimum can change, or the relative order of the maximum and minimum can switch from the maximum leading (following) to the maximum lagging (leading) as the operation progresses.

In some embodiments, the inducing tube waves comprises changing a pump rate so as to induce water hammer.

In some embodiments, the inducing tube waves comprises imparting pressure pulses into the well.

In some embodiments, the pressure pulses may be a frequency or amplitude modulated series, various shape (triangle, sawtooth, sine . . . ) swept frequencies, single frequency pulses, or single impulses.

In some embodiments, the inducing tube waves comprises pumping a fracture treatment into the well.

In some embodiments, on determining the operational anomaly, a warning is communicated to a system operator, the method further comprising performing a mitigation activity corresponding to the determined anomaly.

In some embodiments, the mitigation activity includes changing at least one hydraulic fracture treatment parameter of a fracture treatment.

In some embodiments, the at least one parameter comprises at least one of proppant concentration, proppant density, proppant amount, proppant particle size distribution, proppant particle shape, fluid type/composition, fluid viscosity, fluid viscosity change rate, fluid pumping rate, fluid temperature, fluid chemical composition, chemical additives (e.g., viscosifiers or acids), co-injection of energized gases (nitrogen, CO₂, propane, methane) in both liquid and gas phases, injection of petroleum distillates, or pH of injection fluid (acid/base), fluid pumping pressure, diverter type (if any), perforation schema (perforation location, number of perforations, angle of perforations, size of perforations, depth of perforations), plug type, and stage length.

In some embodiments, the monitoring and mitigation steps are controlled by a microcomputer.

A non-transitory computer readable medium according to another aspect of this disclosure includes logic operable to cause a computer to perform actions. The actions comprise accepting as input to the computer, signals resulting from inducing tube waves in a well during pumping a hydraulic fracture treatment and measuring at least one of pressure and time derivative of pressure in the well; transforming the measurements of at least one of pressure and time derivative of pressure into the cepstrum domain; and detecting an operational anomaly by determining a change in cepstral quefrency corresponding to a two-way travel time of the tube waves in the well.

In some embodiments, the change in cepstral quefrency comprises a maximum value of quefrency.

In some embodiments, the change in cepstral quefrency comprises a minimum value of quefrency.

In some embodiments, the change in cepstral quefrency comprises a sum of a maximum and a minimum value of quefrency.

In some embodiments, the change in cepstral quefrency comprises at least one of peak width, rise time and time offset.

In some embodiments, the inducing tube waves comprises changing a rate of pumping the hydraulic fracture treatment so as to induce water hammer.

In some embodiments, the inducing tube waves comprises imparting pressure changes into the well.

Some embodiments further comprise logic operable to cause the computer to, on determining the operational anomaly, communicating a warning to a system operator.

Some embodiments further comprise logic operable to cause the computer to calculate a mitigation parameter to correct the operational anomaly.

In some embodiments, the at least one mitigation parameter comprises at least one of proppant concentration, proppant density, proppant amount, proppant particle size distribution, proppant particle shape, fluid type/composition, fluid viscosity, fluid viscosity change rate, fluid pumping rate, fluid temperature, fluid chemical composition, chemical additives, co-injection of energized gases in both liquid and gas phases, injection of petroleum distillates, pH of injection fluid, fluid pumping pressure, diverter type, perforation location, number of perforations, angle of perforations, size of perforations, depth of perforations, plug type, and stage length.

Some embodiments further comprise logic operable to cause the computer to implement a machine learning algorithm to identify types of pumping problems and suggest solutions.

In some embodiments, the operational anomaly comprises screenout.

Other aspects and possible advantages will be apparent from the description and claims that follow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a possible well data acquisition setup according to the present disclosure.

FIG. 2 shows input pressure data x(t) or pressure time derivative data (dx/dt) transformed into a power spectrum X²(ƒ). Each column in the lowermost panel in FIG. 2 is the power spectrum of x(t) within a short time window. The peaks in in the power spectrum correspond to resonance events.

FIG. 3 shows the power spectrum of FIG. 2 data transformed into the cepstrum domain. Each column in the lowermost panel is the cepstrum of x(t) in a short time window. The cepstral peak around 7 seconds starting at about 3 minutes represents reflection from fractures near the fracture zone perforations in the well. This reflection is a main event that may be tracked and used in a method according to the present disclosure.

FIGS. 4a, 4b and 4c show simplified models for various borehole conditions, e.g., sand or other proppant accumulating adjacent to perforations with FIG. 4a showing an open boundary condition, FIG. 4b showing a partially open boundary condition, and FIG. 4c showing a closed boundary condition. Note that sand or other proppant can accumulate adjacent to perforations on the well side of a well casing or liner, or on the formation side of the casing or liner, and the accumulated sand or other proppant may partially or completely fill the well.

FIG. 5 shows three typical cepstral peaks obtained from the lowermost panel in FIG. 3 at 100, 115, and 135 min. When the borehole bottom (fracturing region) is under a closed boundary condition, the cepstral peak is positive as shown at line 501. If the borehole bottom becomes open, the cepstral peak changes to negative (black line 502). A partially closed boundary condition response contains both a positive and a negative cepstral peak as shown at line 503. The actual depth of a plug in the wellbore can also be used to estimate the tube wave velocity from the two way travel time.

FIG. 6 shows a time-lapse cepstral scatter plot. The data points are time-coded with time-lapse also shown by arrows. Black is earlier time and lighter gray is later time. The data points around 90-105 minutes fall into the first cluster, shown at 601, in which the cepstral peaks have dominantly negative values. In the second cluster, shown at 602, around 109-120 minutes, the cepstral peaks have both positive and negative values. The third cluster, shown at 603, around 130-150 minutes is dominated by a single positive cepstral peak.

FIG. 7 shows a discriminant function x+y=0. The x-axis represents the minimum value of the cepstral peaks, and the y-axis represents the maximum value of the cepstral peaks. As may be observed in FIGS. 5 and 6, the minimum value x is mostly negative and the maximum value y is likely to be positive. Then, x+y=0 is a useful linear discriminant function [Duda 2001] to classify the data.

FIGS. 8a, 8b and 8c show a combined treatment chart (FIG. 8a ), discriminant function ƒ (FIG. 8b ), and cepstrum plot (FIG. 8c ) with all information time-aligned for pumping of a stage.

FIG. 9 shows an example of screenout detection by using both an x+y plot (left) and x vs. y scatter plot (right).

FIG. 10 shows a flowchart of an example embodiment of a process according to this disclosure.

FIGS. 11a, 11b and 11c show a synthetic demonstration—a model parameter of conductivity is in FIG. 11a and simulated time-lapse tube wave data in FIG. 11b ; time (i) increases from left to right. Each i^(th) column in FIG. 11b is a time series x_(i) (t), and X_(i) ² (ƒ) FIG. 11c is the power spectrum.

FIGS. 12a, 12b and 12c show the time-lapse discriminant chart and cepstrum of the simulated data. The i^(th) column in FIG. 12c is the cepstrum c_(i)(t), where τ is frequency. The event at approximately 7.2 s is a reflection from plug-fractures region in the borehole bottom. The min and max values of this event are tracked and displayed in (12 b).

FIG. 13 shows three typical cepstral peaks cut from FIG. 12c at 2.5 min, 12.5 min, and 23 min, corresponding to times when the simulated data illustrate the response of an open, partially closed, and closed boundary condition, respectively.

FIG. 14 shows the time-lapse cepstral scatter plot generated from the simulated data in 12 b, where horizontal axis is cepstral min and vertical axis is cepstral max. Darker dots are earlier times.

FIG. 15 shows an example embodiment of a computer system that may be used in some embodiments.

DETAILED DESCRIPTION

A method according to the present disclosure may use a variety of signals, including vibrational energy induced by fluid pumping and other operations in a well. Such induced vibrational energy may include “passive signals”, which may otherwise be treated as noise, along with any “active data” (that is, energy which is produced by changes in operations such as pumping rate changes or valve position changes, or deliberately by active processes, e.g., perforation shot firing or pressure pulsing) as input data to monitor the changes in the hydraulic fracturing system. Grêt et al. [Gret 2006] give an example that uses noise (coda waves) to monitor a mining environment. For purposes of a method according to the present disclosure, changes in pump rate or valve position should be of such nature as to induce tube waves in the well, e.g., by causing the change in pump rate and/or valve position to be sufficiently rapid so as to induce water hammer. In other implementations, a pressure pulse generator may be coupled to the well. Such pressure pulse generator should induce tube waves in the well. It is believed that for purposes of a method according to the present disclosure, signals induced by changes in pump rate and/or valve position will be sufficient.

The description below uses specific examples but is not necessarily the only intended or possible implementation or use of the disclosed method. The leading indicators of possible pumping problems described here are identifiable and present before a noticeable change in pressure, which represents the state of the art prior to the present disclosure, is detected.

FIG. 1 is a schematic diagram of an example well data acquisition system that may be used in some embodiments. The system (100) comprises components associated with a well including fluid pump(s) 101, sensors such as hydrophones or pressure transducers 102, a data acquisition and processing apparatus 103, a cased or open well 104, plug or wellbore bottom 106, fracture network 107, and perforations 108. A nearby well 109 may be present in the area of interest. A water hammer pulse 105 may be generated either by the pumps 101 such as by a change in the rate of pumping, or a pressure pulse may be generated by other means as will be described below. Some pulses are the ones generated inherently as part of fluid pumping. Such pulses could be considered “passive” and generally preferred measurement as no additional pressure pulse source is necessary. The pulse(s) will travel and reflect along the well. Nonintrusive sensors, such as pressure transducers, accelerometers, and hydrophone(s), may be disposed in a location on or near the top of the well (e.g., the wellhead) to measure pressure, pressure time derivative and/or particle motion data continuously before, during, and after pumping of a fracture treatment stage. Similar measurements may be made at other points along the well and surface equipment where pressure pulses or pumping noise are detectable.

Signals, such as pressure (p) and pressure time derivative (dp/dt) shown in FIG. 2, which may include both active and passive data, are recorded in this example and may be processed in real time or near real time to extract usable resonances and other events to detect anomalies in the fracture-wellbore system.

To better understand a method according to the present disclosure, the following explanation presents the basis of such method. Let Eq. 1 represent the input data (e.g., pressure time derivative signals) as measured in the well near the wellhead or other suitable location.

x(t)=dp/dt  (Eq. 1)

The input data power spectrum can be calculated by a Fourier Transform (FT) (Eq. 2).

X ²(ƒ)=|FT[x(t)]|²  (Eq. 2)

FIG. 2 in the lowermost panel shows a moving window FT (spectrogram, or waterfall plot) of the input pressure or pressure time derivative signals. Peaks or resonance events can be observed in the lowermost panel. As a matter of technical principle, one may directly use the spectrogram such as shown in FIG. 2 to detect changes in a resonant system. However, for certain situations, it is desirable to further transform the power spectrum into a form that allows easier event detection.

One example of this type of transform is autocorrelation. Another example of such transform is a cepstrum. A cepstrum is the result of taking the inverse Fourier transform of the logarithm of the estimated spectrum of a signal. An inverse Fourier Transform may be used to transform the data into the cepstrum domain (Eq. 3), where τ is the cepstrum quefrency with the unit of time.

c(τ)=IFT ⁻¹[log(X ²(ƒ))]  (Eq. 3)

FIG. 3 in the uppermost and middle panels shows the same input signals as explained with reference to FIG. 2. The lowermost panel in FIG. 3 shows the moving window cepstrum transform (Eq. 3) of the input pressure signals. Reflections or echo events will often appear as peaks in the cepstrum domain, e.g., the event around 7 seconds in quefrency is a reflection from plug-fractures, and the weaker event around 4 seconds is a reflection from a casing and/or liner joint.

FIGS. 4a, 4b and 4c illustrate three examples of well conditions, which may characterize the bottom of a fractured well as open boundary condition (FIG. 4a ), partially open (or partially closed) boundary condition (FIG. 4b ), and closed boundary condition (FIG. 4c ). In FIGS. 4a, 4b and 4c , a change in boundary condition may be related to buildup of sand or other proppant in the well; in other circumstances sand or other proppant may accumulate close to the well (i.e., in the formation or fractures near the wellbore) with relatively little accumulation within the well itself. During normal pumping operations of hydraulic fracturing treatments, the well is open, and proppant and fluid can easily flow through the casing/liner perforations and into the fractures which are being extended into the formation as shown in FIG. 4 a.

Sand or proppant accumulation near casing or liner perforations can result in the boundary condition changing from open to more closed, i.e., partially open as shown in FIG. 4b . In some cases, accumulation of proppant might be more extreme, creating a poor hydraulic conductivity between the well and fractures (low permeability value). Such poor hydraulic conductivity affects the boundary condition. An example of this phenomenon is shown in FIG. 4c , wherein proppant solids fill the well and block the perforations. Blockages may occur in the well, or close to the well in the fractures or perforations, which may be detected as changes in the character of tube wave reflection power spectrum or in the cepstrum of the tube wave reflections. Blockages occurring at a larger distance from the well may not be detectable using tube wave reflections; however they may be detected by other means, for example, an increase in pressure required to maintain a constant rate of fluid injection. For an operator, an open, hydraulically unimpeded wellbore is desirable so pumping a treatment can be completed on schedule at planned rates and proppant loadings.

The tube wave reflections in the pressure data carry information about well conditions; specifically, about the objects that generate the tube wave reflections. In particular, a perforation-fracture peak in the cepstrum transform of the pressure signals can provide information about conditions at the bottom of the well where the tube waves are reflected by the combined reflectivity of the perforations, fractures, and a plug or other well components which isolate deeper sections of the well from the section of the well that is being fractured.

The relative amplitudes and absolute magnitudes of the positive and negative peaks in the cepstrum transform of the pressure signals will depend on the condition of the well bottom. When the cepstral peak has a more positive amplitude, the wellbore is “closed”, while a larger negative amplitude of the cepstral peak indicates an “open” wellbore. A partially open or partially closed well bottom condition will have an intermediate relative amplitude ratio depending on conditions in the well. The lag between the maximum and minimum can change, or the relative temporal order of the maximum and minimum can switch from the maximum leading then following, to the maximum lagging and then leading as the fracture treatment pumping operation progresses.

FIG. 5 shows three cepstral waveforms obtained from the cepstrum transform shown in FIG. 3c at 100, 115, and 135 min. It can be observed in FIG. 5 that cepstral peaks at a time consistent with acoustic tube wave travel time from the top of the well to the perforations and back exhibit significantly different waveforms due to boundary condition changes over time. When hydraulic connectivity between borehole and fractures is low:

the borehole bottom is “closed”,

the acoustic impedance of the combined perforation/fracture/plug system is greater than the acoustic impedance of the well, and

the cepstral peak is positive (curve 501, “Closed” @135 min″ in FIGS. 3 and 5). The open boundary condition, detected by a negative cepstral peak (curve 502, “Open” @100 min” in FIG. 5):

indicates a good connection between the well and fractures, and

the acoustic impedance of the combined perforation/fracture/plug system is smaller than the acoustic impedance of the wellbore.

Partially closed boundary condition can be inferred from a cepstrum transform with limited variation between the positive and negative cepstral peaks, and usually lies between the open and closed boundary condition cepstral peak values (curve 503, “Partially closed@115” min in FIG. 5).

As described above, one example of an attribute that can be monitored in real-time is a positive or negative cepstral peak amplitude relative to a zero value, such as shown in FIG. 5. However, other attributes can be extracted from the cepstral peaks for the purpose of well condition detection. One such attribute is a time delay between a negative or positive peak, e.g., of curve 503, which may be defined as positive if the positive cepstral peak occurs later than the negative peak, or defined as negative if the positive cepstral peak occurs earlier than the negative peak. Additional attributes may include a ratio of positive to negative cepstral peak amplitude relative to a mean cepstral amplitude; or a difference in cepstral amplitude.

A scatter plot shown in FIG. 6, which has a cepstral positive peak on one axis (y), a cepstral negative peak on the other axis (x) plotted with respect to time, can reveal clusters that correspond to all three different boundary conditions. The scatter plot also may provide the advantage of clustering the data points visually. Using color or grayscale coding to track the time at which the x and y values occur may provide information regarding how the well the condition changes with respect to time. In some embodiments, each time point may be represented by a different size dot or other unique symbol, or by other attributes that would indicate relative timing of each datum. Each symbol's attributes may change depending on the length of time since the data were acquired; for example, dots may become increasingly transparent and eventually disappear. The rate of change of the attribute may be controlled by the user.

By viewing the data in different time windows, or causing a sliding time window to be applied so that colors or gray scale shading change and data appear and disappear as the time window moves, it is possible to create a moving visualization of the dynamic variations in well boundary conditions. The speed/rate of change of position on the scatter plot may be used as an indicator of the onset severity of an event and the importance of acting to change operational conditions to avoid unwanted events such as screenout, and may also provide information regarding where the change that causes the event in the well and surrounding volume is occurring. The display as in FIG. 6 can be used to quickly and easily identify the state of the wellbore system with respect to possible pumping problems.

Since passive data are usually noisy and thus have relatively poor quality, the evaluation of attributes must be robust. Cepstral Min (or x) and Max (or y) as shown in FIG. 6 are two robust attributes and can be selected from the peak of waveforms. Thus it is desirable to extract attributes of the detected tube wave reflection events and to display those attributes in other ways such as a two-dimensional time-lapse cepstral scatter plot using the data points (x, y) obtained as shown in FIG. 3. Additionally, FIG. 6 is also an example of time-lapse cepstral scatter plot of cepstral peaks with the darker dots indicating the earlier time and lighter dots later time during pumping operation. The progression is also shown from t=90 minutes through the end with arrows parallel to the measurement points. The data points around 90-105 minutes fall into the first cluster, shown at 601, in which the cepstral peaks have dominantly negative values. In the second cluster, shown at 602, around 109-120 min, the data points have both positive and negative values. The third cluster, shown at 603, around 130-150 minutes is dominated by a positive cepstral peak. A user viewing the plot at various times can be looking on changes during pumping and be forewarned if the peak starts shifting as from 602 to 603.

Other attributes of the cepstral transform of the signals within the time window may also be extracted from the data, such as is known by those skilled in the art of signal analysis. These include various shape attributes, for example, slopes, peak rise time, width, half-power width, and ratio of peak amplitude to width. These can also be plotted on plots such as FIG. 6, either on the x- or y-axis, in color or gray scale, or by varying dot size or shape.

FIG. 7 shows an example embodiment of a cepstral scatter plot using the observations from FIG. 6. A discriminant function x+y=0 is shown in FIG. 7, which may be a useful linear discriminant function to classify the data [Duda 2001].

FIGS. 8a, 8b and 8c show combined data plots using the same input data as used in FIG. 3 during passive and active recording. The pressure, flow rate, and proppant concentration data are shown in FIG. 8a . In the combined plot FIG. 8b, x +y is displayed as a new attribute for comparison to other available time-lapse data, such as pressure, flow rate, proppant concentration, and moving window cepstrum.

Cepstral attributes min (x) and max (y) are displayed in FIG. 9b along with moving window cepstrum FIG. 9a , which is a zoom in of the data shown at the bottom of FIG. 8. It can be observed that the sum x+y increases and crosses zero from 105 to 130 min. The scatter plot shown in FIG. 6 confirms there are three clusters (or three distinguishable borehole conditions) during this period. FIG. 9 is a composite plot using the plots in FIGS. 8a, 8b, 8c and FIG. 6 for an analysis of the pressure and reflection data from 110 min to 130 min. Both the x+y plot (left) and x vs. y scatter plot (right) may be used to detect and predict a screen-out. A fracture screen-out occurred after 130 min (Closed boundary condition). A screen-out precursor is detected around 110 min (Partially Open boundary condition). Other possible applications of this scatter plot include plug slippage detection, casing breach detection, borehole object tracking, and ball seating state detection. In particular, a seated ball will close the plug and result in a closed boundary condition while the cepstral peak is positive. The condition in this example is open, prior to the screenout precursor and screenout onset, and the cepstral peak is more negative than positive.

To implement a method according to the present disclosure, please refer to FIG. 10. FIG. 10 is a flow chart describing an example implementation of a method according to the present disclosure (add hydraulic fracturing supporting operations, e.g., pumping, perforating, etc.) in the following steps:

At 1001, acquire pressure data or pressure time derivative data continuously with a sensor at or near the wellhead (other locations for acquiring pressure or pressure time derivative data are possible, including using a hydrophone string or an optical fiber in the wellbore); During hydraulic fracturing treatment, the sensor(s) are connected and their signals recorded, and the following actions are taken continuously as the data are recorded;

At 1002, transform the time domain pressure or pressure time derivative measurements to the power spectrum X²(f), e.g., by a moving window Fourier Transform (FT); In a microcomputer, the recorded time domain pressure data may be continuously windowed and transformed using a Fourier Transform (FT).

At 1003, transform log[X²(f)] to the cepstrum domain c(T) by Inverse FT, see Eqs. 2-3; Cepstrum transform is continuously generated;

At 1004, track cepstral peaks in the c(T) domain to pick tube wave reflection events; select, visually or by foreknowledge, a time window within which the plug/bottom tube wave reflection peak occurs and then track the cepstrum transform of the pressure data within that time window. The foregoing window changes slowly since tube wave propagation velocity changes are small and well length changes are also small.

At 1005, extract cepstral Min and Max from the tube wave reflection events.

At 1006, display the above extracted Min, and display Min+Max vs. time-lapse to monitor boundary condition changes; other displays of these quantities are possible. Points may be added in real time;

At 1007, use a moving window scatter plot to classify the boundary conditions; According to FIG. 5, 6, or 7, the borehole-fracture system boundary condition can be classified as the one of those described with reference to FIGS. 4a, 4b and 4 c.

At 1008, notify the system operator of the borehole-fracture system boundary status; keep the operator apprised of the ongoing status of the wellbore using a display or other machine-human interface device, for example, using plots such as those in FIG. 9. Provide the operator with ongoing alerts for anomalies, trends, open and closed wellbore-fracture system condition, etc.

At 1009, provide a record of the borehole-fracture system behavior; record and display historical trends, evolution (e.g., as shown in FIG. 9). Identify and alert of anomalies. The anomaly type can be related to the cepstrum location in time and amplitude. Rate of change indicates severity of the onset event.

At 1010, which is optional, use historical data, machine learning, or artificial intelligence to improve the delivery of alerts and mitigation recommendations; machine learning based on previous events or near-screenouts and positive resolution can help recommend to the operator a course of action to mitigate adverse effects (high pressure, screenouts, etc.)

At 1011, adjust fracture treatment parameters in real-time to mitigate adverse effects; This step can be automated in a microcomputer. The operator will adjust treatment parameters in real-time. For example, the operator may reduce proppant loading, reduce pumping rate, change fluid properties to flush out the wellbore and/or fractures of excess sand to establish a proper wellbore-reservoir connection. This will show as a more “open boundary condition” indicator.

The process described with reference to 1001-1011 may be repeated throughout the hydraulic fracturing treatment.

An example embodiment of a data display may be as shown FIG. 8 or 9, but other ways to visually depict the well bottom or entire wellbore system condition are possible.

Alerts, as described with reference to 1008 may be generated indicating types of the anomaly, severity, uncertainty, and possible mitigating actions such as reducing flow rate and proppant concentration, or pump shut-down. The alerts include types of the anomaly, severity, uncertainty, and possible mitigating actions (either artificial intelligence-generated or hard-programmed given certain conditions) such as reducing flow rate and proppant concentration, or shutting pump down.

Implicit in the flowchart description of FIG. 10 is that the information is provided to the operator and can be acted upon and a well treatment adjusted accordingly in real-time.

If mitigation of an adverse condition is warranted, perform such mitigation as deemed appropriate (e.g. reduce rate, reduce proppant loading, etc. and continue the above actions to monitor progress and whether the mitigation approach is working. If the chosen mitigation approach is not working, the operator may choose to adjust additional parameters, including but not limited to modifying proppant concentration, proppant density, proppant amount, proppant particle size distribution, proppant particle shape, fluid type/composition, fluid viscosity, fluid viscosity change rate, fluid pumping rate, fluid temperature, fluid chemical composition, chemical additives (e.g., viscosifiers or acids), co-injection of energized gases (nitrogen, CO₂, propane, methane) in both liquid and gas phases, injection of petroleum distillates, or pH of injection fluid (acid/base), fluid pumping pressure, and diverter type (if any). Additional mitigation, although on a follow up stage may include changes in perforation schema (perforation location, number of perforations, angle of perforations, size of perforations, depth of perforations), plug type, and stage length.

A method according to present disclosure may provide a record of behavior. It will also capture learnings and apply Artificial Intelligence/Machine Learning (AI/ML) to enhance delivery of advice and alerts, for example.

The methodology can be automated and implemented in an apparatus that autonomously performs the above described steps, the monitoring function and event-flagging (at 1007-1009). Moreover, a system can be designed to learn and perform mitigation and monitoring activities automatically and autonomously—either based on simple rules or based on machine learning.

A synthetic data example is described below to demonstrate and verify a screen-out detection method presented in this disclosure. A borehole model was created based on the real data example shown in FIG. 2. There are two sections in the borehole model. The top part is a 3078 m long casing, and the lower part is a 2317 m long liner. The inner diameters of the casing and liner are 0.1186 m and 0.1086 m, respectively. To simulate a screen-out, we assume the borehole boundary condition changes from open to closed, i.e., the conductivity of the fracture-wellbore connection changes from very high to extremely low in 30 minutes. In the simulation the conductivity changes linearly in log scale from 60 to 0.06 (×10⁻¹² m³). Here conductivity is defined as the product of permeability and fracture width.

FIGS. 11a, 11b and 11c show a modeled hydraulic conductivity (FIG. 11a ), the simulated time-lapse tube wave data in the time domain (FIG. 11b ) and in the frequency domain (FIG. 11c ). Events in FIG. 11b are tube wave reflections within the well. It can be observed that the waveforms of the reflections change as hydraulic conductivity decreases. If the conductivity is high (e.g., at time before 7 min), successive reflections reverse polarities, for example, the event at 8-10 seconds is negative (black) then positive (white) and the event at 16-17 seconds is positive then negative at early time-lapse, then all events become positive then negative at late time-lapse when conductivity is low. The events in FIG. 11b can also be thought of as resonances. The resonant frequencies decrease as the hydraulic conductivity changes from large to small. The resonant amplitudes have a sharp drop near 12 min when the screen-out occurs. Although it is possible to detect the screen-out with resonances, according to the present disclosure it is more suitable to use cepstrum to detect the screen-out.

Cepstrum calculated using an inverse Fourier transform, i.e., Eq. 3. FIGS. 12a, 12b and 12c show, respectively, the model parameters, the cepstrum min and min+max, and the time-lapse cepstrum. The event around 7.2 s in FIG. 12c is a cepstral peak that represents the reflection from the plug-fractures near borehole bottom; the time corresponds to the 2-way time of the tube wave in the wellbore, which allows estimating this time from the well length and tube wave velocity. The cepstral peak changes from negative (dark) to positive (bright) as conductivity decreases. The polarity change is slow at first, rapid over the interval near 12 minutes, when screen-out occurs, and then slower after the transition. The min and max values of the cepstral peak are traced and displayed in FIG. 12b in the forms of cepstral min and cepstral min+max. Cepstral min+max=0 may be used as a threshold to flag the screen-out.

In order to view the details of the cepstrum, three time indications, around 2.5, 12.5, and 23 min in FIG. 12c , are extracted and plotted in FIG. 13. Those three indications represent open, partially closed, and closed boundary conditions, respectively. It can be clearly observed that the open boundary condition (or large conductivity) results in a negative cepstral peak, and the closed boundary condition results in a positive peak. The polarity of the cepstral peaks, therefore, may be a robust indicator for the boundary condition that is directly related to screen-out.

FIG. 14 shows cepstral scatter plot, where the horizontal axis is cepstral min and the vertical axis is cepstral max. The location in this scatter plot reveals the condition of the wellbore connection, as detailed in FIG. 7. The scatter locations can help reveal different boundary conditions. FIG. 14. is an example of relatively faster speed of change in boundary condition compared to FIG. 6 where the change in boundary conditions from partially closed to closed occurred in about 20 min. For the situation revealed in FIG. 6, the operator could have recovered by reducing the injection rate and/or proppant concentration in order to recover the operation to normal condition without shutting down the pumps. If the onset was much faster, the operator would have to shut down the pump or drop rate and proppant concentration more aggressively to avoid a screenout. Synthetic data, such as shown in FIGS. 11-14, may be generated to simulate various events that may occur in a wellbore, and the behaviors used to train or program a machine to perform autodetection of event severity and rapidity.

The results of the synthetic data example and the real data example are consistent. Both real data and synthetic data show that (1) the cepstral peaks change from positive to negative when a screen-out occurs, (2) cepstral min and max are two robust features, and (3) the time-lapse cepstral scatter plot is a useful tool to view the course of a screen-out. In some cases, changes that occur rapidly might be handled differently than changes that occur slowly.

FIG. 15 shows an example computing system 1500 in accordance with some embodiments that may be used to implement a method according to the disclosure. The computing system 1500 may be an individual computer system 1501A or an arrangement of distributed computer systems. The individual computer system 1501A may include one or more analysis modules 1502 that may be configured to perform various tasks according to some embodiments, such as the tasks explained with reference to FIG. 15. To perform these various tasks, the analysis module 1502 may operate independently or in coordination with one or more processors 1504, which may be connected to one or more storage media 1506. A display device 1505 such as a graphic user interface of any known type may be in signal communication with the processor 1504 to enable user entry of commands and/or data and to display results of execution of a set of instructions according to the present disclosure.

The processor(s) 1504 may also be connected to a network interface 1508 to allow the individual computer system 1501A to communicate over a data network 1510 with one or more additional individual computer systems and/or computing systems, such as 1501B, 1501C, and/or 1501D. Note that computer systems 1501B, 1501C and/or 1501D may or may not share the same architecture as computer system 1501A, and may be located in different physical locations, for example, computer systems 1501A and 1501B may be at a well drilling location, while in communication with one or more computer systems such as 1501C and/or 1501D that may be located in one or more data centers on shore, aboard ships, and/or located in varying countries on different continents.

A processor may include, without limitation, a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device.

The storage media 1506 may be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of FIG. 15 the storage media 1506 are shown as being disposed within the individual computer system 1501A, in some embodiments, the storage media 1506 may be distributed within and/or across multiple internal and/or external enclosures of the individual computing system 1501A and/or additional computing systems, e.g., 1501B, 1501C, 1501D. Storage media 1506 may include, without limitation, one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; optical media such as compact disks (CDs) or digital video disks (DVDs); or other types of storage devices. Note that computer instructions to cause any individual computer system or a computing system to perform the tasks described above may be provided on one computer-readable or machine-readable storage medium, or may be provided on multiple computer-readable or machine-readable storage media distributed in a multiple component computing system having one or more nodes. Such computer-readable or machine-readable storage medium or media may be considered to be part of an article (or article of manufacture). An article or article of manufacture can refer to any manufactured single component or multiple components. The storage medium or media can be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions can be downloaded over a network for execution.

It should be appreciated that computing system 1500 is only one example of a computing system, and that any other embodiment of a computing system may have more or fewer components than shown, may combine additional components not shown in the example embodiment of FIG. 15, and/or the computing system 1500 may have a different configuration or arrangement of the components shown in FIG. 15. The various components shown in FIG. 15 may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.

Further, the acts of the processing methods described above may be implemented by running one or more functional modules in information processing apparatus such as general purpose processors or application specific chips, such as ASICs, FPGAs, PLDs, or other appropriate devices. These modules, combinations of these modules, and/or their combination with general hardware are all included within the scope of the present disclosure.

References cited in the present disclosure:

-   [1] Grêt, A., Snieder, R, U Özbay, 2006, Monitoring in situ stress     changes in a mining environment with coda wave interferometry:     Geophysical Journal International -   [2] Dunham, E., Zhang, J., Quan Y., Harris, J., and Kaitlyn Mace,     2017, Hydraulic fracture conductivity inferred from tube wave     reflections: SEG Annual Meeting. -   [3] Parkhonyuk, S., Fedorov, Kabannik, A., Korkin, R., Nikolaev, M.,     and Tsygulev, I., 2018, Measurements While Fracturing: Nonintrusive     Method of Hydraulic Fracturing Monitoring, Presented at the SPE     Hydraulic Fracturing Technology Conference & Exhibition held in The     Woodlands, Tex., SPE-189886-MS -   [4] Duda, R., Hart, P, and Stork, D., 2001, Pattern Classification,     2nd Edition: Wiley Interscience.

Although only a few examples have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the examples. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. 

What is claimed is:
 1. A method for detecting operating anomalies during hydraulic fracturing, comprising: inducing tube waves in a well during pumping a hydraulic fracture treatment; measuring at least one of pressure and time derivative of pressure in the well; transforming the measured at least one of pressure and time derivative of pressure into the cepstrum domain; and detecting an operational anomaly by determining a change in cepstral quefrency corresponding to a two-way travel time of the tube waves in the well.
 2. The method of claim 1 wherein the change in cepstral quefrency comprises a maximum value of quefrency.
 3. The method of claim 1 wherein the change in cepstral quefrency comprises a minimum value of quefrency.
 4. The method of claim 1 wherein the change in cepstral quefrency comprises a sum of a maximum and a minimum value of quefrency.
 5. The method of claim 1 wherein the change in cepstral quefrency comprises at least one of peak width, rise time and time offset.
 6. The method of claim 1 wherein the inducing tube waves comprises changing a rate of pumping the hydraulic fracture treatment so as to induce water hammer.
 7. The method of claim 1 wherein the inducing tube waves comprises imparting pressure changes into the well.
 8. The method of claim 1 wherein on determining the operational anomaly, a warning is communicated to a system operator, the method further comprising performing a mitigation activity corresponding to the determined anomaly.
 9. The method of claim 8 wherein the mitigation activity includes comprises changing at least one parameter of a hydraulic fracture treatment.
 10. The method of claim 9 wherein the at least one mitigation parameter comprises at least one of proppant concentration, proppant density, proppant amount, proppant particle size distribution, proppant particle shape, fluid type/composition, fluid viscosity, fluid viscosity change rate, fluid pumping rate, fluid temperature, fluid chemical composition, chemical additives, co-injection of energized gases in both liquid and gas phases, injection of petroleum distillates, pH of injection fluid, fluid pumping pressure, diverter type, perforation location, number of perforations, angle of perforations, size of perforations, depth of perforations, plug type, and stage length.
 11. The method of claim 9 wherein the monitoring and mitigation steps are controlled by a microcomputer.
 12. The method of claim 9 wherein a machine learning algorithm is applied to identify types of pumping problems and suggest solutions.
 13. The method of claim 1 wherein a visual tracking is provided to a system operator.
 14. The method of claim 1 wherein the operational anomaly comprises screenout.
 15. A non-transitory computer readable medium comprising logic operable to cause a computer to perform actions comprising: accepting as input to the computer, signals resulting from inducing tube waves in a well during pumping a hydraulic fracture treatment and measuring at least one of pressure and time derivative of pressure in the well; transforming the measurements of at least one of pressure and time derivative of pressure into the cepstrum domain; and detecting an operational anomaly by determining a change in cepstral quefrency corresponding to a two-way travel time of the tube waves in the well.
 16. The non-transitory computer readable medium of claim 15 wherein the change in cepstral quefrency comprises a maximum value of quefrency.
 17. The non-transitory computer readable medium of claim 15 wherein the change in cepstral quefrency comprises a minimum value of quefrency.
 18. The non-transitory computer readable medium of claim 15 wherein the change in cepstral quefrency comprises a sum of a maximum and a minimum value of quefrency.
 19. The non-transitory computer readable medium of claim 15 wherein the change in cepstral quefrency comprises at least one of peak width, rise time and time offset.
 20. The non-transitory computer readable medium of claim 15 wherein the inducing tube waves comprises changing a rate of pumping the hydraulic fracture treatment so as to induce water hammer.
 21. The non-transitory computer readable medium of claim 15 wherein the inducing tube waves comprises imparting pressure changes into the well.
 22. The non-transitory computer readable medium of claim 15 further comprising logic operable to cause the computer to, on determining the operational anomaly, communicating a warning to a system operator.
 23. The non-transitory computer readable medium of claim 22 further comprising logic operable to cause the computer to calculate a mitigation parameter to correct the operational anomaly.
 24. The non-transitory computer readable medium of claim 23 wherein the at least one mitigation parameter comprises at least one of proppant concentration, proppant density, proppant amount, proppant particle size distribution, proppant particle shape, fluid type/composition, fluid viscosity, fluid viscosity change rate, fluid pumping rate, fluid temperature, fluid chemical composition, chemical additives, co-injection of energized gases in both liquid and gas phases, injection of petroleum distillates, pH of injection fluid, fluid pumping pressure, diverter type, perforation location, number of perforations, angle of perforations, size of perforations, depth of perforations, plug type, and stage length.
 25. The non-transitory computer readable medium of claim 24 further comprising logic operable to cause the computer to implement a machine learning algorithm to identify types of pumping problems and suggest solutions.
 26. The non-transitory computer readable medium of claim 15 wherein the operational anomaly comprises screenout. 